How do you prove Sec^2θ+tan^2θ=sec^4θ-tan^4θ ?

1 Answer
Noah G
Mar 26, 2018

See below.

Explanation:

We have:

#sec^2theta + tan^2theta = (sec^2theta - tan^2theta)(sec^2theta + tan^2theta)#

#sec^2theta + tan^2theta = (1/cos^2theta - sin^2theta/cos^2theta)(1/cos^2theta + sin^2theta/cos^2theta)#

#sec^2theta + tan^2theta = ((1- sin^2theta)/cos^2theta)((1 + sin^2theta)/cos^2theta)#

#sec^2theta + tan^2theta = (cos^2theta)/cos^2theta((1 + sin^2theta)/cos^2theta)#

#sec^2theta + tan^2theta = sec^2theta + tan^2theta#

#LHS = RHS#

As required!

Hopefully this helps!

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